Noooo wait! DO change 100% of the water once a week! Also change 50% mid week. This is an excellent tested and proven successful formular for betta keeping by OldFishLady. prepare water before hand is good, try to have he new water the same temperature as the old. or it will shock the poor fish.
He does not need a filter, it will do nothing for him in a 1 gallon, and he wont appreciated the current in the small area. until you purchase a heater, put him in the warmest part of your house with a stable temperature.
You donot really need any aquarium gravel. gravel is another hassel to clean.
Never clean with soap. just rinse with hot water when cleaning the Jar.
After you purchase the heater, make sure you are raising the temperature slowly.
Don't over clean :) stick to the water change schedules and you should be fine
Also recommended feeding is twice a day, 2 pellets/feeding. treats such as freeze dried blood worms once a week instead of pellets. And one food free day.